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A continuous-time formulation of an adaptive critic design (ACD) is investigated. Connections to the discrete case are made, where backpropagation through time (BPTT) and real-time recurrent learning (RTRL) are prevalent. Practical benefits are that this framework fits in well with plant descriptions given by differential equations and that any standard integration routine with adaptive step-size does an adaptive sampling for free. A second-order actor adaptation using Newton's method isdoi:10.1109/tnn.2006.889499 pmid:17526332 fatcat:v5msmlbvnvaorifzzihuzmr6fi